Combined Inverse Kinematic and Static Analysis and Optimal Design of a Cable-Driven Mechanism with a Spring Spine

Abstract

A special humanoid neck with low motion noise requirements yields a cable-driven parallel mechanism to imitate the rotational motion of a human neck. The fixed base and moving platform of the mechanism are connected by four cables and a column compression spring. The four cables are actuated separately, while the spring can support weight on the moving platform. Although similar mechanisms exist in the literature, the analysis of them is scarce because a flexible spring instead of a rigid kinematic chain is used as the spine. With the spring’s lateral buckling motion, a new approach must be adopted to solve the kinematics. In this paper, we propose a method that combines the kinematics with the statics to solve them simultaneously. The configuration of the moving platform is parameterized with four parameters, one of which is considered as parasitic motion. Using the spring’s lateral buckling equation, we can obtain the parasitic motion and solve the inverse position problem. The optimal design for cable placements is then performed to minimize the actuation force. The method in this paper provides a novel way to analyze parallel mechanisms with a spring spine and it can be applied to other mechanisms with flexible spines.     

CAT4 (Cable Actuated Truss—4 Degrees of Freedom): A Novel 4 DOF Cable Actuated Parallel Manipulator

The CAT4 (Cable Actuated Truss—4 degrees of freedom) robot is a novel, passively jointed, parallel robot utilizing six control cables for actuation. The architecture has been under development at the Queen's University Robotics Laboratory. The robot utilizes a passive jointed linkage with 18 revolute joints to constrain the end effector motion and provide the desired structural stability, restricting the end effector to 3 translational degrees of freedom (DOF) and 1 DOF for end effector pitch. This central mechanism together with winched cable actuation gives a number of important benefits for applications where the advantages of a parallel robot are required in conjunction with light weight. Six electric motor driven winches control the length of the cable actuators that extend from the top frame to points on the end effector raft and jointed linkage to create a stiff, but lightweight, actuated robot. Simulation work on the robot is presented giving the kinematics, including a computational estimate of the workspace for a specific configuration. Results of computational simulation of the motion of the manipulator and a discussion of the advantages and potential difficulties are also presented. © 2002 Wiley Periodicals, Inc.     

拟人机器人TH-1手臂运动学

拟人机器人手臂的主要特点是它的运动功能，能够实现握手、行走时掌握平衡等动作．本文 主要针对自行设计的具有转摆结构的拟人机器人TH-1手臂机构进行了运动学分析，为其控 制提供数学基础．提出了坐标变换、三角变换等方法，巧妙求解出拟人机器人TH-1手臂逆 向运动学的解析表达式．建立了仿真软件平台，验证了运动学正逆向方程的有效性．     

Conceptual design and analysis of the 2T1R mechanism for a cooking robot

This paper deals with the design and analysis of a two-translation and one-rotation (2T1R) mechanism for a novel cooking robot. Firstly the motions involved in stir-fry, the most representative operation in the cooking processes used in Chinese cuisine, are analyzed in details. Then the featured motions are decomposed into four main movements that are used as a design base for a wok motion mechanism. Several three-degrees-of-freedom (DOF) parallel manipulators are considered. From these, a 2T1R mechanism is selected as an ideal candidate. A 4-DOF (2T1R+1T) cooking robot is constructed by combining the 2T1R parallel manipulator with a 1-DOF linear feed mechanism. It is shown that the combined 4-DOF robot can perform the required cooking operations, particularly the stir-fry. The analysis conducted on the proposed 2T1R parallel manipulator includes inverse kinematics, forward kinematics, the velocity analysis, the constant orientation workspace, and the total orientation workspace. A prototype of the cooking robot is developed. The experiments verify that the proposed cooking robot is suitable for performing the required operations.     

A Humanoid Neck System Featuring Low Motion-Noise

This paper presents our recently developed humanoid neck system that can effectively mimic motion of human neck with very low motion noises. The features of low motion noises allows our system to work like a real human neck. Thus the level of acoustic noises from wearable equipments, such as donning respirators or chemical-resistant jackets, induced by human head motion can be simulated and investigated using such a system. Our low motion-noise humanoid head/neck system is based on the spring structure, which can generate 1 degree of freedom (DOF) jaw movement and 3DOF neck movement. To guarantee the low-noise feature, no noise-makers like gear and electro-driven parts are embedded in the head/neck structure. Instead, the motion is driven by seven polyester cables, and the actuators pulling the cables are sealed in a sound insulation box. Furthermore, statics analysis and motion control design of the system have been presented. Experimental results clearly show that the head/neck system can greatly mimic the motion of human head with an A-weighted noise level of 30 dB or below.     

3-CPS并联机器人的机构分析及仿真研究

由于传统Stewart平台有支链运动耦合和工作空间小的缺点,因此以串并联混合机构形式,提出一种新型的六自由度并联机构。为解决运动耦合和工作空间小的问题,并且在保证运动精度的前提下降低生产成本,主要运用矩阵代数工具分析了该机构的反向运动学,运用数值迭代解法分析了该机构的正向运动学,并对该机构的速度加速度进行了分析。通过Adams仿真软件对运动学模型进行数值验证及分析,深入研究了该机构的运动特性和线性度,实验结果证明这种机构具有运动解耦特性和旋转对称性,可以进行良好的线性运动。通过Matlab仿真软件分析对机构驱动器的误差进行研究,实验结果证明该机构用于天文望远镜支撑平台时,保证动平台的运动精度的同时降低了生产成本。     

基于直齿轮传动和双环解耦的柔性手腕原理与运动学分析

由于ｐｉｔｃｈ、ｙａｗ运动耦合干涉问题一直没有被提出和解决，使得现有的柔性手腕机构中必须采用复杂、加工困难的球齿轮传动以满足ｐｉｔｃｈ、ｙａｗ机构运动的特殊要求．基于作者提出的双环解耦原理解决了不需球齿轮传动实现ｐｉｔｃｈ－ｙａｗ－ｒｏｌ柔性腕机构的关键问题，因而采用通常的直齿圆柱齿轮传动方式不需特殊加工即避开了球齿轮传动复杂和加工困难的问题．此外，提出和设计的柔性手腕在机器人柔性臂设计方面也有参考价值．     

Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator

In this study, a 4-degree-of-freedom (DOF) serial robot manipulator was designed and developed for the pick-and-place operation of a flexible manufacturing system. The solution of the inverse kinematics equation, one of the most important parts of the control process of the manipulator, was obtained by using four different optimization algorithms: the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, the quantum particle swarm optimization (QPSO) algorithm and the gravitational search algorithm (GSA). These algorithms were tested with two different scenarios for the motion of the manipulator’s end-effector. One hundred randomly selected workspace points were defined for the first scenario, while a spline trajectory, also composed of one hundred workspace points, was used for the second. The optimization algorithms were used for solving of the inverse kinematics of the manipulator in order to successfully move the end-effector to these workspace points. The four algorithms were compared according to the execution time, the end-effector position error and the required number of generations. The results showed that the QPSO could be effectively used for the inverse kinematics solution of the developed manipulator.     

基于人体运动的仿人型机器人动作的运动学匹配

提出了仿人型机器人模仿人体运动的相似性函数,讨论了运动学约束,并给出了满足运动约束条件且具有与人体动作高相似性的运动求解算法. 在有33个自由度的仿人型机器人实体上完成了模仿人的太极拳动作,验证了方法的有效性.     

Rotation and direction judgment from visual images head-slaved intwo and three degrees-of-freedom

The contribution to spatial awareness of adding a roll degree-of-freedom (DOF) to telepresence camera platform yaw and pitch was examined in an experiment, where subjects judged direction and rotation of stationary target markers in a remote scene. Subjects viewed the scene via head-slaved camera images in a head-mounted display. Elimination of the roll DOF affected rotation judgment, but only at extreme yaw and pitch combinations, and did not affect azimuth and elevation judgment. Systematic azimuth overshoot occurred regardless of roll condition. Observed rotation misjudgments are explained by kinematic models for eye-head direction of gaze     

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing.     

3-RRRT并联机器人位置正向求解研究

研究一种3-RRRT型并联机器人机构的运动学正向求解方法。根据3-RRRT型并联机器人机构特点以及关节运动的取值范围，提出了以并联机器人支链中支杆的方向余弦和动平台绝对位置坐标为系统的广义坐标的方法，并详细地推导了3-RRRT型并联机器人运动学模型，通过进一步消除中间变量的方法最终获得了易于正、逆运动学求解的只包含3个驱动关节坐标与动平台3个绝对位置坐标的约束方程组。最后，运用基于Moore—Penwse广义逆的牛顿迭代格式编制了MATLAB运动学正向求解程序，并进行了运动学正向求解数值仿真，结果表明求解程序快速有效。     

Exact solution to the inverse kinematics problem of a standard 6-axis robot manipulator

Presented are four sets of exact solutions for the vector of the joint angles {θ_i} pertaining to the inverse kinematics problem of a standard 6-axis robot manipulator with two different kinds of gripper configurations. Here a standard 6-axis robot is meant to be a general computer-controlled revolute robot with base, shoulder, elbow, wrist pitch, wrist yaw, wrist roll, and gripping action. Explicit solutions are obtained using Denavit-Hartenberg homogeneous transformations. Furthermore, the inverse solutions are examined by means of a direct kinematic computer program.     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.     

仿人机器人复杂动作设计中人体运动数据提取及分析方法

提出了仿人机器人复杂动作设计中人体运动数据提取及分析方法. 首先, 通过运动捕捉系统获取人体运动数据, 并采用运动重定向技术, 输出人--机简化模型的数据; 然后, 对运动数据进行分析和运动学解算, 给出基于人体运动数据的仿人机器人逆运动学求解方法, 得到仿人机器人模型的关节角数据; 再经过运动学约束和稳定性调节后, 生成能够应用于仿人机器人的运动轨迹. 最终, 通过在仿人机器人BHR-2上进行刀术实验验证了该方法的有效性.     

Kinematic analysis of a flexible six-DOF parallel mechanism.

In this paper, a new type of six-degrees of freedom (DOF) flexible parallel mechanism (FPM) is presented. This type of parallel mechanism possesses several favorable properties: (1) its number of DOFs is independent of the number of serial chains which make up the mechanism; (2) it has no kinematical singularities; (3) it is designed to move on rails, and therefore its workspace is much larger than that of a conventional parallel manipulator; and (4) without changing the number of DOFs and the kinematics of the mechanisms, the number of the serial chains can be reconfigured according to the needs of the tasks. These properties make the mechanism very preferable in practice, especially for such tasks as joining huge ship blocks, in which the manipulated objects vary dramatically both in weights and dimensions. Furthermore, the mechanism can be used as either a fully actuated system or an underactuated system. In the fully actuated case, the mechanism has six DOF motion capabilities and manipulation capabilities. However, in the underactuated case, the mechanism still has six DOF motion capabilities, but it has only five DOF manipulation capabilities. In this paper, both the inverse and forward kinematics are studied and expressed in a closed form. The workspace and singularity analysis of the mechanism are also presented. An example is presented to illustrate how to calculate the kinematics of the mechanism in both fully-actuated and underactuated cases. Finally, an application of such a mechanism to manufacturing industry is introduced.     

Inverse Kinematics Based Human Mimicking System using Skeletal Tracking Technology

Humanoid robots needs to have human-like motions and appearance in order to be well-accepted by humans. Mimicking is a fast and user-friendly way to teach them human-like motions. However, direct assignment of observed human motions to robot’s joints is not possible due to their physical differences. This paper presents a real-time inverse kinematics based human mimicking system to map human upper limbs motions to robot’s joints safely and smoothly. It considers both main definitions of motion similarity, between end-effector motions and between angular configurations. Microsoft Kinect sensor is used for natural perceiving of human motions. Additional constraints are proposed and solved in the projected null space of the Jacobian matrix. They consider not only the workspace and the valid motion ranges of the robot’s joints to avoid self-collisions, but also the similarity between the end-effector motions and the angular configurations to bring highly human-like motions to the robot. Performance of the proposed human mimicking system is quantitatively and qualitatively assessed and compared with the state-of-the-art methods in a human-robot interaction task using Nao humanoid robot. The results confirm applicability and ability of the proposed human mimicking system to properly mimic various human motions.     

Case study: Inertial measurement unit calibration platform

The Department of Mechanical Engineering and the Avionics Engineering Center at Ohio University are developing an electromechanical system for the calibration of an inertial measurement unit (IMU) using global positioning system (GPS) antennas. The GPS antennas and IMU are mounted to a common platform to be oriented in the angular roll, pitch, and yaw motions. Vertical motion is also included to test the systems in a vibrational manner. A 4‐DOF system based on the parallel carpal wrist is under development for this task. High‐accuracy positioning is not required from the platform since the GPS technology provides absolute positioning for the IMU calibration process. © 2000 John Wiley & Sons, Inc.     

Backward Ladder Climbing Locomotion of Humanoid Robot with Gain Overriding Method on Position Control

We studied ladder climbing locomotion with the humanoid robot, DRC‐HUBO, under the constraints suggested by DARPA. Considering the hardware constraints of the robot platform, we planned for the robot to climb backward with four limbs moving separately. Task‐priority whole‐body inverse kinematics was used to generate and track the motion while maintaining COM inside the support polygon. As ladder climbing is a multicontact motion that generates interaction and internal forces, we resolved these issues using a gain overriding method applied to the position control of the motor controllers. This paper also provides various vision methods and posture modification strategies for the restricted conditions of the challenge. We ultimately verified our work in the DRC trials by getting a full score on the ladder task.     

Hybrid head mechanism of the groundhog-like mine rescue robot

Since mining accidents severely threaten production safety, robotic assistant systems can play an important role by searching and rescuing survivors in hostile underground environments. Accordingly, this paper focuses on the design, modeling and optimization of a 4UPS+PU spatial hybrid manipulator, which serves as the dexterous head section of a quadrupedal, groundhog-like mine rescue robot. This biologically inspired mechanism has three degrees of freedom (DOF), one translation and two rotations. Additionally, a passive leg is connected to both centers of the base and the moving platform in order to constrain undesirable motion. In order to evaluate the operational capacity, an analysis of the mobility and the inverse kinematics are conducted. The reachable workspace is generated with a boundary-searching discretization approach, and the local and global performance atlas, including stiffness and dexterity, are investigated. The multi-population evolution of structural and behavioral parameters is implemented to seek the optimal dexterity of the hybrid head mechanism.